Washington
— With less than three weeks to go, the United States and the Soviet Union are stepping up public and private diplomacy, each sending signals that it wants the summit to be successful and trying its best to achieve that result. President Reagan yesterday announced that he has instructed US negotiators in Geneva to present a new proposal in response to Moscow's recent arms offer.

The new US proposal covers the three areas of arms control: strategic nuclear weapons; intermediate-range weapons; and devices to defend against attack, including systems in space. Without disclosing any details, Mr. Reagan characterized the proposal as calling for ``deep cuts, no first-strike capability, defense research, and no cheating.''

The US is also asking the Soviet Union to extend the current round of negotiations in Geneva, which were scheduled to end today. And Reagan has written to allied leaders and to Soviet leader Mikhail Gorbachev concerning the new US proposal, which he described as ``serious and detailed.''

In meeting with the White House press, the President said the recent Soviet arms reduction offer ``falls significantly short in several key areas.'' But he repeated his recent statement at the United Nations which said the Soviet offer has ``certain positive seeds which need to be nurtured.''

As US Secretary of State George P. Shultz leaves tomorrow for talks in Moscow with Mr. Gorbachev, there were also other developments adding to momentum now building toward the superpower summit:

The President was interviewed in the Oval Office yesterday by four Soviet journalists who are international-affairs experts. The interview is expected to be published Sunday in the Soviet newspaper Izvestia, which would be unusual in a country with a tightly controlled press.

Moscow in recent days has made other gestures. These include a decision to permit Yelena Bonner, wife of exiled Soviet dissident Andrei D. Sakharov, to seek medical treatment in the West. Also, an offer to stop construction on the Soviet radar installation near Krasnoyarsk, in Siberia -- a facility the US says violates the ABM Treaty -- in return for US cancellation of plans to improve radar stations in Greenland and Britain.

Differences between Washington and Moscow on arms control are so deep that the two leaders are not expected to reach a full-blown agreement at the summit meeting Nov. 19-20. But it is hoped that the two will agree on a general set of principles or framework to guide the Geneva negotiators and meet again sometime to sign a pact.

Among the items Mr. Shultz is reported to be taking up with Soviet officials next week is the possibility of a second summit meeting. Sen. John W. Warner (R) of Virginia, who was part of a congressional delegation that met Mr. Gorbachev earlier this year, has been quoted as saying he (Warner) expects such a follow-up summit meeting within 18 months.

Intense debate has been under way in the administration concerning how to respond to Moscow's arms proposal. The plan calls for a 50 percent cut in strategic offensive arms of both superpowers in return for an end to development and testing of the President's antimissile defense program, or so-called ``star wars.'' The administration regards the proposal as one-sided. Disagreements center on weapons that would be included in the strategic category, the size of the reduction, and the method of countin g future sublimits on various categories of weapons.

The President has been under growing pressure from the Western allies and lawmakers in Congress to show flexibility on the arms question, and a substantive American counterproposal is bound to be favorably received in both quarters.

``Reagan does want a successful summit, and he wants to carry Congress and the allies along,'' says an administration official. ``So in arms control it has to be recognized that the Soviet proposal for a reduction to 6,000 weapons and a 50 percent reduction in delivery systems is an important offer. The rest is junk, but we need to build on what is important.''

At the same time the administration continues to press points in addition to arms control issue, stressing that the US is equally interested in the other items on its agenda -- regional issues, bilateral issues, and human rights. These will be raised by Mr. Shultz in Moscow.

One official involved in the summit planning says no progress has been made so far between the two sides on human rights or on regional issues. Some bilateral agreements, such as a new cultural and scientific exchange agreement, are well along, he adds. Others, including an agreement to renew air service, are ``still up in the air.''

Mr. Reagan's interview with the Soviet journalists was the first by an American President since November 1961, when John F. Kennedy was interviewed at his home in Hyannisport, Mass., by the editor of Izvestia. The administration offered to make Reagan available to the Soviet press several weeks after Time magazine carried an interview with Gorbachev.

Moscow's offer to stop contruction on the Krasnoyarsk radar has been greeted coolly here. Administration officials say the US radars at Thule, Greenland, and Fylingdales, England, are permissible under the 1972 ABM treaty because they are pointed inward and are not intended to play a role in attacking Soviet missiles.